choose all true statements about composite function:

Question

f(g(h(I(x)))) is a valid composite function

f(g(x))=g(f(x))

(fog)(x)=f(g(x))

(3fo2g)(x) is a valid composite function

f(f(x)) is a valid composite function

Answer 1

f(g(h(I(x)))) is a valid composite function, when this assumption is true:

f, g, h, I are real valued functions of a single real variable.

I will continue assuming that below.

f(g(x))=g(f(x)) is not true for all f, g.

For example, it is not true for these:

f(x) = x+1

g(x) = 2x

(fog)(x)=f(g(x)) is true, because it is the definition of fog

(3fo2g)(x) is normally not a valid composite function.

It could be made valid, it it were interpreted as meaning (3fo(2g))(x)

f(f(x)) is a valid composite function